This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. MATHEMATICAL MODELING AND SIMULATION Subproject Description As a Center, we have established expertise in the area of simulation in bioelectric fields, have built on that expertise in the current funding period, and propose to continue to make this form of simulation a centerpiece of our future research activities. At the start of the Center our focus was on passive electrical characteristics of the torso and head and their response to endogenous bioelectric sources (the heart and brain);we solved both forward problems, based on known sources, as well as inverse problems, in which we sought to identify and localize bioelectric sources from measurements on (or outside) the body surface. We have continued this research thrust through the current year and propose to continue it in the next funding cycle, working closely with collaborators. In recent years, we have also begun to simulate bioelectric activity itself and thus to study the nature of bioelectric sources;these sources are highly dynamic and increased knowledge of their behavior will help improve our ability to predict the consequences of their function and dysfunction in disease. We propose to continue this research, with emphasis on simulating the effects of myocardial ischemia and defibrillation on the heart and epilepsy and deep brain stimulation in the brain. In order to translate the discoveries and computational developments within the Center to the broader biomedical user community, we will continue to develop, publish, release, and support software that will incorporate models of dynamic bioelectric sources as well as the tools with which to create efficient solutions to the associated forward and inverse problems. One application of the simulation of bioelectric activity has been in the computation of the spread of excitation in microscopic models of myocardial tissue. The goal of this research was to address a longstanding gap in the multiscale modeling of cardiac electrophysiology between the very evolved and well-characterized behavior of cardiac cell membranes and the simulation of electrical activity in the whole heart. Simulation of the heart has advanced mainly because there exist models at each of the meaningful scales from stochastic models of ion channels to the whole heart and torso. However, there is a need for simplification at each transition of scale, and hence a requirement that results at one scale are established as an associated expression at the next scale. For example, a model of tissue must be able to incorporate the effects of changes in the behavior of the cell in order to mimic or predict pathophysiology or the mechanisms of pharmaceutics. It is also essential[unreadable]and until recently a significant omission[unreadable]in this translation across scales, that changes in microscopic structure find expression in tissue level models. We have begun to address this omission. In addition, within this TRD we have begun to explore the use of acceleration hardware such as graphical processing units, GPU's, and, in general, streaming architectures for use in biomedical simulation. As the speed and efficiency of GPU's grows at rates even faster than those of conventional central processing units (CPU's), there is a growing consensus that the streaming architecture embodied in most modern graphics processors has inherent advantages in scalability.